This is a non-relativistic description. The correct relativistic description assigns quantum field operators to events in spacetime, and operators at spacelike separated events commute--i.e., they give the same results regardless of which order they occur in. So there is no physical fact of the matter about the order in which the particles "change state".
It's worth noting that the full explanation given here assumes that the many-worlds interpretation is correct, which not all physicists would agree with. But the "no-communication theorem" is true independently of which interpretation of QM you adopt.
You can't transport information through quantum entanglement.